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Describe the transformation from the parent function f(x) = x³ to the function g(x) = (x + 5)³.

User Reisclef
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Final answer:

The function g(x) = (x + 5)³ represents a horizontal translation of the parent function f(x) = x³, shifting it 5 units to the left without any other transformations such as stretching or reflecting.

Step-by-step explanation:

The transformation from the parent function f(x) = x³ to the function g(x) = (x + 5)³ is a horizontal translation. In general, if we have a function f(x) and we create a new function g(x) = f(x - d), this represents a translation of the graph of f(x) d units to the right. Conversely, if we have g(x) = f(x + d), this represents a translation d units to the left. Therefore, the function g(x) = (x + 5)³ is the cube function shifted 5 units to the left. There are no other transformations such as stretching, shrinking, or reflecting over any axis in this particular transformation.

User Ameena
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